What is the integral of x(1+2x^4) ?

The integral of x(1+2x^4) is (x^2)/2+(x^6)/3+C

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integral of x(1+2x^4)

\int x (1 + 2 x^{4}) d x

\frac{x ^{2}}{2} + \frac{x ^{6}}{3} + C

Solution steps

\int x (1 + 2 x^{4}) d x

Expand

x (1 + 2 x^{4}) : x + 2 x^{5}

= \int x + 2 x^{5} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x d x + \int 2 x^{5} d x

\int x d x = \frac{x ^{2}}{2}

\int 2 x^{5} d x = \frac{x ^{6}}{3}

= \frac{x ^{2}}{2} + \frac{x ^{6}}{3}

Add a constant to the solution

= \frac{x ^{2}}{2} + \frac{x ^{6}}{3} + C

\frac{\partial}{\partial x} (4 x^{3} y^{2} + 3)

y = ln (2 x + 1)

\frac{d}{d x} (lo g_{2} (2 x^{2} - 7 x + 1))

\int 4 x e^{9 x} d x

f (x) = x^{4} - 5 x^{2} - x, at x = 1

What is the integral of x(1+2x^4) ?
The integral of x(1+2x^4) is (x^2)/2+(x^6)/3+C